Sperm Retrieval in Patients with Klinefelter Syndrome: A Skewed Regression Model Analysis

Background The most common chromosomal abnormality due to non-obstructive azoospermia (NOA) is Klinefelter syndrome (KS) which occurs in 1-1.72 out of 500-1000 male infants. The probability of retrieving sperm as the outcome could be asymmetrically different between patients with and without KS, therefore logistic regression analysis is not a well-qualified test for this type of data. This study has been designed to evaluate skewed regression model analysis for data collected from microsurgical testicular sperm extraction (micro-TESE) among azoospermic patients with and without non-mosaic KS syndrome. Materials and Methods This cohort study compared the micro-TESE outcome between 134 men with classic KS and 537 men with NOA and normal karyotype who were referred to Royan Institute between 2009 and 2011. In addition to our main outcome, which was sperm retrieval, we also used logistic and skewed regression analyses to compare the following demographic and hormonal factors: age, level of follicle stimulating hormone (FSH), luteinizing hormone (LH), and testosterone between the two groups. Results A comparison of the micro-TESE between the KS and control groups showed a success rate of 28.4% (38/134) for the KS group and 22.2% (119/537) for the control group. In the KS group, a significantly difference (P<0.001) existed between testosterone levels for the successful sperm retrieval group (3.4 ± 0.48 mg/mL) compared to the unsuccessful sperm retrieval group (2.33 ± 0.23 mg/mL). The index for quasi Akaike information criterion (QAIC) had a goodness of fit of 74 for the skewed model which was lower than logistic regression (QAIC=85). Conclusion According to the results, skewed regression is more efficient in estimating sperm retrieval success when the data from patients with KS are analyzed. This finding should be investigated by conducting additional studies with different data structures.


Introduction
The most common chromosomal abnormality due to non-obstructive azoospermia (NOA) is Klinefelter syndrome (KS) which occurs in genetic abnormality can develop meiotic nondisjunction due to a 47,XXY genotype in the majority of cases (4). KS is characterized by infertility, elevated luteinizing hormone (LH) levels, elevated follicle stimulating hormone (FSH), normal or reduced testosterone, normal or increased height, muscle weakness and reduced strength, increased facial hair, osteoporosis, obesity, increased thromboembolic risk, dyslipidemia, and low glucose tolerance. In addition of cognition, but without an increase in the occurrence of mental retardation (5). Although the typical karyotype is 47,XXY, chromosomal complements with multiple X chromosomes such as 48XXXY.
It is important to evaluate the chances for sperm retrieval among KS patients and compare them to azoospermia with normal karyotype by results for researchers. When researchers have method to handle this problem and patients may not need to undergo invasive surgeries (6). On the other hand, it can also increase the chances for success and decrease patient expenses. Logistic and probit regressions have already been applied to analyze binary outcome data. The function. However, the use of such distributions may give biased results in some cases. The purpose of this study is to apply the skewed regression model, as a new regression model, (7) to analyze data collected by microsurgical testicular sperm extraction (micro-TESE) among azoospermic patients with and without non-mosaic KS syndrome who referred to Royan Institute due to infertility. This type of regression has a further parameter, the skewness parameter, controls the skewness of the link function. Finally, we have compared results from the two models (logistic regression and skewed regression) according to statistical criteria.

Materials and Methods
This cohort study enrolled 134 patients with KS and 537 patients without KS. Patients were referred to Royan Institute, a referral infertility clinic in Tehmatched patients and controls according to disease duration, time of surgery, and surgeon in order to avoid confounding factors such as surgical skills and age.
cytes. Semen analysis was performed according to World Health Organization (WHO) guidelines to evaluate sperm parameters. At least two analysamples were taken in the morning to measure FSH, LH, and testosterone levels.
Microsurgical testicular sperm extraction (Micro-TESE) was performed on the patients under general anesthesia as described by Schlegel (8). The procedure was considered successful when sperm were retrieved from the patients.
The binary logistic regression model, as previously introduced (9), is appropriate for independent outcomes. When y 1 , y 2 , …,y n are a set of n observations of binaryoutcomes such as success and failure in sperm retrieval, which are independent of each other; p_i is the probability of success forpatient "i"; x 1 , x 2 ,…, x n are independent predic-1 2 k are equal to regression coefwritten as follows: is acumulative distribution function. If F is the distribution function of normal and logistic, then the above model will be alogistic and probit regression model, respectively.
Assume that a binary outcome "Y it Chehrazi et al.
is measured for a particular person during time T. As the outcomes for one person are correlated, in order toevaluate the relationship betweenindependent variables and theoutcome, the earlier model is no longer appropriate. There are different methods to model a relationship between a correlated binary outcome and a set of independent variables. In this study, we have focused on a mixed generalized lin- where b_i is a random effect with normal distribution in this formula. Adding this term into model 1 enables the observations to be considered independently. In model 2, which is similar to the independent model, symmetrical logistic or normal distribution functions are assumed for F.
Asymmetric links are used for regression models regression model as previously introduced by Chen et al. (7) is explained. This model uses a hidden variable structure, which has been introduced by Albert desired cut-off point as zero on a continuous latent variable with a mixed structure. The hidden variables can have distributions such as the logistic or normal. Symmetric or a symmetric distributions can be produced for the variable through a mixed structure. Various asymmetric links also can be produced in this way. The most important property of Chen's model is that it considers the problem of "skewness", which controls amount of skewness of a link. The link will be symmetric if skewness is zero.
Data were analyzed by R software (version 3.2.2) using the BB package and GEE pack for asymmetric and symmetric models, respectively. The logistic regression model with the symmetquasi Akaike's information criteria (QAIC) (11).  (Table 1).

Results
We performed a marginal effect logistic regression analysis with serum FSH, LH, testosterone, age, and patient groups to determine an association between the probability of sperm retrieval and the covariates during micro-TESE. Adjusted association from the model showed that probability of retrieving sperm during micro-TESE did not differ between the two groups (control and KS) after adjusting for the covariates and could not be predicted by any of the variables. On the other hand, the results obtained from skewed logistic regression showed that the probability of retrieving sperm was not the same for patients with and without KS symmetric link was equal to 85, whereas for an asymmetric link it was 74. The results of comparing the regression model are shown in Table 2. The proportion of sperm retrieval was almost equal between patients with and without KS.

Discussion
The present study has compared sperm retrieval in azoospermia patients with and without KS by two regression models. Sperm from KS patients is typically retrieved by conventional TESE and micro-TESE techniques. Although both techniques have successfully retrieved sperm in 44% of patients, a comparison between conventional TESE and micro-TESE showed that micro-TESE had a higher success rate (55%) compared to conventional TESE (44%) (12). Sperm retrieval rate in men with KS by micro-TESE ranged from approximately 21-72% (13-19). A study by Maof 38.5% among non-mosaic KS patients. Possibly the rate of sperm retrieval in the current nonmosaic KS series (28.4%) could be compared with those previously reported. A pilot study proposed that sperm retrieval rates in adolescents with KS could be compared with those reported in older men (21).
In some studies it was found that the sperm recovery rate in men with KS reduced with increased age, however there were no effects on serum FSH, LH, or testosterone levels (22-25). Medical and ethical issues were mentioned related to sperm retrieval in adolescent males with KS in a study by Okada et al. (26). Whether previous testosterone treatment, could be considered or not be as a barrier in the sperm retrieval. In our study, skewed logistic regression showed that only younger men had a higher sperm recovery rate compared to older men which suggested that aging could reduce successful sperm recovery in men with KS. In the KS group, a comparison of laboratory parameters between men with successful sperm retrieval and those with failed sperm relevel in patients with successful sperm retrieval without KS no difference existed between age, FSH, LH, and testosterone levels in patients who experienced successful sperm retrieval compared to those with failed sperm retrieval. Our study reported higher sperm retrieval rates in patients with KS compared to the control group, which could be related to confounder distribution in the two groups and their associations with the outcome. The skewed regression was more powerful than logistic regression to detect this relation. 22, 23). This result has shown that KS patients can be hopeful for sperm detection and subsequent pregnancy outcomes.
We used logistic regression with symmetric and asymmetric links for data analysis. To the best of plied a regression model with asymmetric link in reproduction research and in this group of infertile patients. The incorrect use of asymmetric link instead of an asymmetric link could lead to a poor els. Therefore, the QAIC value was lower and has symmetric link (27, 28). In addition, sometimes it is not possible to control all confounding factors. Hence, the confounding effects should be adjusted provide a more accurate result. The importance of such studies more than ever.

Conclusion
gression model with an asymmetric link is more regression has modeled data from infertility studies, we recommend that additional studies and analyses be conducted to evaluate how well this notice, sperm could be retrieve of non-mosaic KS as well as without KS patients.